Data Collection and Sampling

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Data Collection and Sampling

• Chapter 5

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Recall

• Statistics is a tool for converting data into
  information

• But
• Where then does data come from?
• How is it gathered?
• How do we ensure its accurate(??)? Is the data
  reliable(??)?
• Is it representative(???) of the population from
  which it was drawn?
• This chapter explores some of these issues.

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5.1 Methods of Collecting Data

• The reliability and accuracy of the data affect
  the validity of the results of a statistical
  analysis.
• The reliability and accuracy of the data depend
  on the method of collection.
• Four of the most popular sources of statistical
  data are
• Published data(????)
• Observational studies(??)
• Experimental studies(??)
• Surveys(??)

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Published Data

• This is often a preferred source of data due to
  low cost and convenience.
• Published data is found as printed material,
  tapes, disks, and on the Internet.
• Data published by the organization that has
  collected it is called PRIMARY DATA(????).

For example Data published by the US Bureau of
Census.

• For example
• The Statistical abstracts of the United States,
• compiles data from primary sources
• Compustat, sells variety of financial data
  tapescompiled from primary sources

• Data published by an organization different than
  the organization that has collected it is called
  SECONDARY DATA(????).

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Observational and experimental studies

• When published data is unavailable, one needs to
  conduct a study to generate the data.

• Observational study is one in which measurements
  representing a variable of interest are observed
  and recorded, without controlling any factor that
  might influence their values.
• Experimental study is one in which measurements
  representing a variable of interest are observed
  and recorded, while controlling factors(????)
  that might influence their values.

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Surveys

• Surveys solicit information from people. e.g.
  pre-election polls marketing surveys.
• The Response Rate(???) (i.e. the proportion of
  all people selected who complete the survey) is a
  key survey parameter.
• Surveys can be made by means of
• personal interview(????)
• telephone interview(????)
• self-administered questionnaire(??????)

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Questionnaire Design(????)

• Key design principles of a good questionnaire
• Keep the questionnaire as short as possible.
• Ask short, simple, and clearly worded questions.
• Start with demographic questions to help
  respondents get started comfortably.
• Use dichotomous (yesno) and multiple choice
  questions.
• Use open-ended questions cautiously.
• Avoid using leading-questions.
• Pretest a questionnaire on a small number of
  people.
• Think about the way you intend to use the
  collected data when preparing the questionnaire.

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5.2 Sampling(??)

• Recall that statistical inference permits us to
  draw conclusions about a population based on a
  sample.
• Motivation for conducting a sampling procedure
• Costs. (e.g. its less expensive to sample 1,000
  television viewers than 100 million TV viewers)
• Population size.
• The possible destructive nature (???)of the
  sampling process. (e.g. performing a crash test
  on every automobile produced is impractical).
• The sampled population(????) and the target
  population(????) should be similar to one another.

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5.3 Sampling Plans

• A sampling plan is just a method or procedure for
  specifying how a sample will be taken from a
  population.
• We will focus our attention on these three
  methods
• Simple random sampling(??????)
• Stratified random sampling(??????)
• Cluster sampling(????)

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Simple Random Sampling

• In simple random sampling all the samples with
  the same size are equally likely to be chosen.
• To conduct random sampling
• assign a number to each element of the chosen
  population (or use already given numbers),
• randomly select the sample numbers (members). Use
  a random numbers table, or a software package.

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Simple Random Sampling

• Example 5.1
• A government income-tax auditor is responsible
  for 1,000 tax returns.
• The auditor will randomly select 40 returns to
  audit.
• Use Excels random number generator to select
  the returns.
• Solution
• We generate 50 numbers between 1 and 1000 (we
  need only 40 numbers, but the extra might be used
  if duplicate numbers are generated.)

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Simple Random Sampling

• Example 5.1 A government income tax auditor must
  choose a sample of 40 of 1,000 returns to audit

Extra s may be used if duplicate random numbers
are generated.
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Simple Random Sampling
Round-up
X(100)
383 101 597 900 885 959 15 408 864 139 2
46 . .
The auditor should select 40 files numbered
383, 101, ...
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Stratified Random Sampling

• This sampling procedure separates the population
  into mutually exclusive sets (strata) (?????),
  and then draw simple random samples from each
  stratum.

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Stratified Random Sampling

• With this procedure we can acquire information
  about
• the whole population
• each stratum
• the relationships among strata.

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Stratified Random Sampling

• After the population has been stratified, we can
  use simple random sampling to generate the
  complete sample. For example, keep the proportion
  of each stratum in the population.

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Cluster Sampling

• Cluster sampling is a simple random sample of
  groups or clusters of elements.
• This procedure is useful when
• it is difficult and costly to develop a complete
  list of the population members (making it
  difficult to develop a simple random sampling
  procedure.
• the population members are widely dispersed
  geographically.
• Cluster sampling may increase sampling
  error(????), because of probable similarities
  among cluster members.

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Sample Size(???)

• Numerical techniques for determining sample sizes
  will be described later, but suffice it to say
  that the larger the sample size is, the more
  accurate we can expect the sample estimates to be.

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5.4 Sampling and Non-Sampling Errors

• Two major types of error can arise when a sample
  of observations is taken from a population
• Sampling error(????) refers to differences
  between the sample and the population that exist
  only because of the observations that happened to
  be selected for the sample.
• Nonsampling errors (?????) are more serious and
  are due to mistakes made in the acquisition of
  data or due to the sample observations being
  selected improperly.

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Sampling Error

• Sampling error refers to differences between the
  sample and the population that exist only because
  of the observations that happened to be selected
  for the sample.
• Another way to look at this is the differences
  in results for different samples (of the same
  size) is due to sampling error
• E.g. Two samples of size 10 of 1,000 households.
  If we happened to get the highest income level
  data points in our first sample and all the
  lowest income levels in the second, this delta is
  due to sampling error.
• Increasing the sample size will reduce this type
  of error.

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Sampling Errors
Population income distribution
m ( population mean)
Sampling error
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Nonsampling Error

• Nonsampling errors are more serious and are due
  to mistakes made in the acquisition of data or
  due to the sample observations being selected
  improperly.
• Three types of nonsampling errors
• Errors in data acquisition
• Nonresponse errors(?????)
• Selection bias(????)
• Note increasing the sample size will not reduce
  this type of error.

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Errors in data acquisition

• arises from the recording of incorrect
  responses, due to
• incorrect measurements being taken because of
  faulty equipment,
• mistakes made during transcription from primary
  sources,
• inaccurate recording of data due to
  misinterpretation of terms, or
• inaccurate responses to questions concerning
  sensitive issues.

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Data Acquisition Error
Population
Sampling error Data acquisition error
Sample
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Nonresponse Error

• refers to error (or bias) introduced when
  responses are not obtained from some members of
  the sample, i.e. the sample observations that are
  collected may not be representative of the target
  population.
• As mentioned earlier, the Response Rate (i.e. the
  proportion of all people selected who complete
  the survey) is a key survey parameter and helps
  in the understanding in the validity of the
  survey and sources of nonresponse error.

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Non-Response Error
Population
No response here...
may lead to biased results here.
Sample
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Selection Bias

• occurs when the sampling plan is such that some
  members of the target population cannot possibly
  be selected for inclusion in the sample.

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Selection Bias
Population
When parts of the population cannot be selected...
the sample cannot represent the whole population.
Sample